A hawk flying at an altitude of $121 \mathrm {~m}$ accidentally drops its prey. The parabolic trajectory of the falling prey is described by the equation
$$y = 121 - \frac { x ^ { 2 } } { 64 }$$
until it hits the ground, where $y$ is its height above the ground and $x$ is the horizontal distance traveled in meters.
True or False?
The distance traveled by the prey from the time it is dropped until the time it hits the ground is approximately $156.532 \mathrm {~m}$.

Question

Quizplus · Accepted Answer

To find the distance traveled by the prey, we need to find the horizontal distance traveled by the prey from the time it is dropped until the time it hits the ground. This is the distance corresponding to the width of the parabolic trajectory.

The equation of the parabolic trajectory is given by 
$$y = 121 - \frac { x ^ { 2 } } { 64 }$$

Solving for $x$ when $y=0$, we get
$$0 = 121 - \frac { x ^ { 2 } } { 64 }$$
$$x^2=7744$$
$$x=\pm 88$$

Since the question is only asking for the distance traveled and not the displacement, we take the positive value of $x$ as the distance traveled. Hence, the distance traveled by the prey from the time it is dropped until the time it hits the ground is $88\mathrm{~m}$.

Therefore, the statement "The distance traveled by the prey from the time it is dropped until the time it hits the ground is approximately $156.532 \mathrm {~m}$" is false.

A Hawk Flying at an Altitude Of 121 m121 \mathrm {~m}121 m Accidentally Drops Its Prey

A Hawk Flying at an Altitude Of $121 \mathrm {~m}$ Accidentally Drops Its Prey